Amplitude analysis of $ψ(3686)$ radiative decays into $π^{0} π^{0}$ system
A model-independent amplitude analysis of the $π^{0} π^{0}$ system produced in radiative $ψ(3686)$ decays is presented. The analysis is based on the unique dataset of $(2712.4\pm14.3)\times10^6$ $ψ(3686)$ decays collected by the BESIII detector. Scalar and tensor partial-wave contributions are obtained as piecewise functions of $M_{\text{inv}}(π^{0} π^{0})$ with minimal model assumptions. The observed contribution of the scalar partial wave exhibits similar behavior to the one reported in the study of radiative $J/ψ$ decays, while the tensor contributions provide no evidence for resonance-like structures except for the clearly visible $f_2(1270)$. The results are presented in the form of log-likelihood scans in $M_{\text{inv}}(π^{0} π^{0})$ bins, which preserve all the statistical information and account for relevant systematic uncertainties. The model-independent description provided in this paper allows to combine the presented results with other related data in the development of phenomenological models.